The Cosmological Origin of the Tully-Fisher Relation

We use high-resolution cosmological simulations that include the effects of gasdynamics and star formation to investigate the origin of the Tully-Fisher relation in the standard cold dark matter cosmogony. Stars are assumed to form in collapsing, Jeans-unstable gas clumps at a rate set by the local gas density and the dynamical/cooling timescale. The energetic feedback from stellar evolution is assumed to heat the gas-surrounding regions of ongoing star formation, where it is radiated away very rapidly. The star formation algorithm thus has little effect on the rate at which gas cools and collapses, and, as a result, most galaxies form their stars very early. Luminosities are computed for each model galaxy using their full star formation histories and the latest spectrophotometric models. We find that the stellar mass of model galaxies is proportional to the total baryonic mass within the virial radius of their surrounding halos. Circular velocity then correlates tightly with the total luminosity of the galaxy, which reflects the equivalence between mass and circular velocity of systems identified in a cosmological context. The slope of the relation steepens slightly from the blue to the red bandpasses and is in fairly good agreement with observations. Its scatter is small, decreasing from ~0.38 mag in the U band to ~0.24 mag in the K band. The particular cosmological model we explore here seems unable to account for the zero point of the correlation. Model galaxies are too faint at z=0 (by about 2 mag) if the circular velocity at the edge of the luminous galaxy is used as an estimator of the rotation speed. The model Tully-Fisher relation is brighter in the past by ~0.7 mag in the B band at z=1, which is at odds with recent observations of z~1 galaxies. We conclude that the slope and tightness of the Tully-Fisher relation can be naturally explained in hierarchical models, but that its normalization and evolution depend strongly on the star formation algorithm chosen and on the cosmological parameters that determine the universal baryon fraction and the time of assembly of galaxies of different mass.